Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 3$ and $ BC = 2x + 39$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 3} = {2x + 39}$ Solve for $x$ $ 6x = 42$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({7}) - 3$ $ BC = 2({7}) + 39$ $ AB = 56 - 3$ $ BC = 14 + 39$ $ AB = 53$ $ BC = 53$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {53} + {53}$ $ AC = 106$